Subgroups — #34444934

Order 20224.

718 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098995	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₁₂₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#23775087	C₂	1	2	yes	maximal, complemented
4	#23765661	C₂	1	1	yes	maximal, characteristic, complemented
5	#23765491	C₂	1	1	yes	maximal, characteristic, complemented
6	#23765486	C₂	1	1	yes	maximal, characteristic, complemented
7	#23765456	C₂	1	2	yes	maximal, complemented
8	#23765331	C₂	1	2	yes	maximal, complemented
9	#23765325	C₂	1	2	yes	maximal, complemented
10	C₄×D₁₂₆₄	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579183	C₂²	1	2	yes	complemented
13	C₂²×D₆₃₂	C₂²	1	2	yes	—
14	#19099209	—	2	2	no	—
15	#19098995	—	2	4	no	—
16	C₂×Dic₆₃₂	C₂²	1	1	yes	characteristic, complemented
17	C₂×#14579106	C₂²	1	2	yes	complemented
18	C₂×#14579106	C₂²	1	2	yes	complemented
19	C₂×D₁₂₆₄	—	2	4	no	—
20	C₂×D₁₂₆₄	C₂²	1	2	yes	—
21	C₂×D₁₂₆₄	C₂²	1	1	yes	characteristic
22	C₂×D₁₂₆₄	C₂²	1	1	yes	characteristic
23	#19098947	C₂²	1	2	yes	complemented
24	#19098804	C₂²	1	2	yes	—
25	#19098799	C₂²	1	2	yes	complemented
26	#19098779	—	2	2	no	—
27	#19098716	—	2	2	no	—
28	#19098710	—	2	2	no	—
29	C₄×D₆₃₂	C₂²	1	2	yes	complemented
30	#19098389	C₂²	1	1	yes	characteristic, complemented
31	#19098368	C₂²	1	2	yes	complemented
32	#19098365	C₂²	1	2	yes	complemented
33	#19098365	C₂²	1	2	yes	complemented
34	C₂²×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
35	C₂²×C₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
36	C₈×D₄×C₇₉	C₂²	1	1	yes	characteristic
37	C₄⋊C₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
38	C₂²⋊C₁₆×C₇₉	C₂²	1	1	yes	characteristic
39	C₂²⋊C₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×#11929624	—	2	2	no	—
42	C₂²×D₃₁₆	—	2	2	no	—
43	#14579183	—	2	4	no	—
44	#14579183	—	4	2	no	—
45	C₂×Dic₃₁₆	C₂³	1	2	yes	—
46	C₂×#11929613	—	2	2	no	—
47	C₂×#11929613	—	2	2	no	—
48	C₂×D₆₃₂	—	2	4	no	—
49	C₂×D₆₃₂	—	2	2	no	—
50	C₂×D₆₃₂	—	4	2	no	—
51	C₂×D₆₃₂	C₂³	1	2	yes	—
52	C₂×D₆₃₂	C₂³	1	2	yes	—
53	#14579149	—	2	2	no	—
54	#14579146	—	4	2	no	—
55	#14579140	—	2	2	no	—
56	#14579135	—	2	2	no	—
57	#14579134	—	4	2	no	—
58	#14579129	—	4	2	no	—
59	C₄×D₃₁₆	—	2	2	no	—
60	C₂²⋊C₄×D₇₉	—	4	2	no	—
61	Dic₆₃₂	—	2	2	no	—
62	#14579106	—	2	4	no	—
63	#14579106	—	4	2	no	—
64	D₁₂₆₄	—	2	2	no	—
65	D₁₂₆₄	—	2	4	no	—
66	D₁₂₆₄	D₄	1	4	yes	complemented
67	#14579095	C₂³	1	2	yes	—
68	#14579086	—	2	2	no	—
69	#14579083	—	2	2	no	—
70	#14579083	—	2	2	no	—
71	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
73	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
74	C₂×C₁₆×C₇₉	—	2	2	no	—
75	C₂×C₁₆×C₇₉	—	2	2	no	—
76	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
77	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
79	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₇₉	D₄	1	1	yes	characteristic
81	C₂²⋊C₈×C₇₉	D₄	1	1	yes	characteristic
82	C₂²⋊C₈×C₇₉	D₄	1	1	yes	characteristic
83	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
84	C₂³×D₇₉	—	4	2	no	—
85	#11929624	—	4	4	no	—
86	#11929624	—	8	2	no	—
87	C₂×Dic₁₅₈	—	2	2	no	—
88	C₂×D₃₁₆	—	2	2	no	—
89	C₂×D₃₁₆	—	2	2	no	—
90	C₂×D₃₁₆	—	4	4	no	—
91	C₂×D₃₁₆	—	4	2	no	—
92	C₂×D₃₁₆	—	8	2	no	—
93	C₂×C₂²⋊D₇₉	—	4	2	no	—
94	C₂×C₂²⋊D₇₉	—	4	2	no	—
95	C₂×C₄×D₇₉	—	4	2	no	—
96	C₂×C₄×D₇₉	—	4	2	no	—
97	Dic₃₁₆	—	2	2	no	—
98	Dic₃₁₆	—	2	2	no	—
99	#11929613	—	4	4	no	—
100	#11929613	—	8	2	no	—
101	D₆₃₂	—	2	2	no	—
102	D₆₃₂	—	2	2	no	—
103	D₆₃₂	—	2	2	no	—
104	D₆₃₂	—	4	4	no	—
105	D₆₃₂	C₂×D₄	1	4	yes	—
106	C₄⋊Dic₇₉	—	2	2	no	—
107	Dic₇₉⋊C₄	—	4	2	no	—
108	C₂²⋊Dic₇₉	—	4	2	no	—
109	(C₂×D₇₉)⋊C₄	—	4	2	no	—
110	(C₂×D₇₉)⋊C₄	—	4	2	no	—
111	(C₂×D₇₉)⋊C₄	—	4	2	no	—
112	(C₂×D₇₉)⋊C₄	—	4	2	no	—
113	C₂×D₄×C₇₉	D₈	1	1	yes	characteristic
114	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₇₉	—	2	1	no	—
117	C₂×C₈×C₇₉	—	2	1	no	—
118	C₂×C₈×C₇₉	—	2	1	no	—
119	C₂×C₈×C₇₉	—	2	1	no	—
120	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
124	C₄⋊C₄×C₇₉	D₈	1	1	yes	characteristic
125	C₂²⋊C₄×C₇₉	D₈	1	1	yes	characteristic
126	C₂²⋊C₄×C₇₉	D₈	1	1	yes	characteristic
127	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₁₆×C₇₉	—	2	1	no	—
129	C₁₆×C₇₉	—	2	1	no	—
130	C₁₆×C₇₉	—	2	1	no	—
131	C₁₆×C₇₉	C₂×D₄	1	2	yes	—
132	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
133	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
134	C₂²×D₇₉	—	4	2	no	—
135	C₂²×D₇₉	—	4	2	no	—
136	C₂²×D₇₉	—	8	4	no	—
137	C₂²×D₇₉	—	8	4	no	—
138	C₂²×D₇₉	—	16	2	no	—
139	D₄×C₇₉	—	2	2	no	—
140	C₂×C₄×C₇₉	—	2	1	no	—
141	C₂×C₄×C₇₉	—	2	1	no	—
142	C₂×C₄×C₇₉	—	2	1	no	—
143	C₂×C₄×C₇₉	—	2	1	no	—
144	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
146	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
149	C₂²⋊D₇₉	—	8	4	no	—
150	C₂²⋊D₇₉	—	16	2	no	—
151	C₂×Dic₇₉	—	4	2	no	—
152	C₂×Dic₇₉	—	4	2	no	—
153	D₃₁₆	—	2	4	no	—
154	D₃₁₆	—	4	2	no	—
155	D₃₁₆	—	4	2	no	—
156	D₃₁₆	—	4	2	no	—
157	D₃₁₆	—	8	4	no	—
158	C₄×D₇₉	—	8	4	no	—
159	C₄×D₇₉	—	16	2	no	—
160	Dic₁₅₈	—	4	2	no	—
161	Dic₁₅₈	—	4	2	no	—
162	C₈×C₇₉	—	2	1	no	—
163	C₈×C₇₉	—	2	1	no	—
164	C₈×C₇₉	—	2	1	no	—
165	C₈×C₇₉	C₂²×D₄	1	1	yes	characteristic
166	C₈×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂²×C₇₉	—	2	1	no	—
168	C₂²×C₇₉	—	2	1	no	—
169	C₂²×C₇₉	—	2	1	no	—
170	C₂²×C₇₉	—	2	1	no	—
171	C₂²×C₇₉	—	2	1	no	—
172	C₂²×C₇₉	#508	1	2	yes	complemented
173	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
174	C₂×D₇₉	—	4	4	no	—
175	C₂×D₇₉	—	8	2	no	—
176	C₂×D₇₉	—	8	2	no	—
177	C₂×D₇₉	—	8	2	no	—
178	C₂×D₇₉	—	8	2	no	—
179	C₂×D₇₉	—	8	2	no	—
180	C₂×D₇₉	—	16	8	no	—
181	C₄×C₇₉	—	2	1	no	—
182	C₄×C₇₉	—	2	1	no	—
183	C₄×C₇₉	—	2	1	no	—
184	C₄×C₇₉	—	2	1	no	—
185	C₄×C₇₉	D₄²	1	1	yes	characteristic
186	C₄×C₇₉	#576	1	1	yes	characteristic
187	Dic₇₉	—	8	2	no	—
188	Dic₇₉	—	8	2	no	—
189	#33846	—	79	1	no	maximal, Sylow
190	C₂×C₇₉	—	2	2	no	—
191	C₂×C₇₉	—	4	1	no	—
192	C₂×C₇₉	D₄×D₈	1	1	yes	characteristic
193	C₂×C₇₉	C₂×#508	1	1	yes	characteristic
194	C₂×C₇₉	#3415	1	1	yes	characteristic
195	D₇₉	—	8	4	no	—
196	D₇₉	—	16	2	no	—
197	C₂×#508	—	79	1	no	—
198	C₂²×D₁₆	—	79	1	no	—
199	#3280	—	79	2	no	—
200	#2249	—	79	1	no	—
201	#2216	—	79	1	no	—
202	#2215	—	79	1	no	—
203	#2210	—	79	2	no	—
204	#2187	—	79	2	no	—
205	#2186	—	79	2	no	—
206	C₄×D₁₆	—	79	1	no	—
207	D₄×C₁₆	D₇₉	1	1	yes	characteristic, complemented
208	C₇₉	#33846	1	1	yes	characteristic, complemented, Sylow
209	C₂×#135	—	79	2	no	—
210	C₂²×D₈	—	79	2	no	—
211	#546	—	158	2	no	—
212	#508	—	158	4	no	—
213	C₂×Q₃₂	—	79	1	no	—
214	C₂×SD₃₂	—	79	2	no	—
215	C₂×SD₃₂	—	79	2	no	—
216	C₂×D₁₆	—	79	1	no	—
217	C₂×D₁₆	—	79	2	no	—
218	C₂×D₁₆	—	79	1	no	—
219	C₂×D₁₆	—	158	4	no	—
220	C₂²×C₁₆	C₂×D₇₉	1	1	yes	characteristic
221	C₂²×C₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
222	#495	—	79	2	no	—
223	#467	—	79	2	no	—
224	#466	—	79	2	no	—
225	#463	—	158	2	no	—
226	#450	—	158	2	no	—
227	#449	—	158	2	no	—
228	C₄×D₈	—	79	2	no	—
229	C₈×D₄	C₂×D₇₉	1	1	yes	characteristic
230	#366	—	79	1	no	—
231	C₄⋊C₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
232	#358	—	79	2	no	—
233	#357	—	79	2	no	—
234	#357	—	79	2	no	—
235	C₂²⋊C₁₆	C₂×D₇₉	1	1	yes	characteristic
236	C₂²⋊C₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
237	C₄×C₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
238	C₂×#41	—	158	2	no	—
239	C₂²×D₄	—	158	2	no	—
240	#135	—	316	2	no	—
241	#135	—	158	4	no	—
242	C₂×Q₁₆	—	79	2	no	—
243	C₂×SD₁₆	—	158	2	no	—
244	C₂×SD₁₆	—	158	2	no	—
245	C₂×D₈	—	316	2	no	—
246	C₂×D₈	—	79	2	no	—
247	C₂×D₈	—	79	2	no	—
248	C₂×D₈	—	158	4	no	—
249	C₂×D₈	—	158	2	no	—
250	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
251	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
252	#124	—	158	2	no	—
253	#123	—	316	2	no	—
254	C₂²⋊Q₈	—	158	2	no	—
255	#121	—	316	2	no	—
256	#121	—	158	2	no	—
257	#120	—	316	2	no	—
258	C₄×D₄	—	158	2	no	—
259	C₄×D₄	D₃₁₆	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	—	316	2	no	—
261	Q₃₂	—	158	2	no	—
262	SD₃₂	—	316	2	no	—
263	SD₃₂	—	158	4	no	—
264	D₁₆	—	79	4	no	—
265	D₁₆	—	158	4	no	—
266	D₁₆	—	158	2	no	—
267	C₂×C₁₆	—	2	2	no	—
268	C₂×C₁₆	—	2	2	no	—
269	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
270	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
271	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
272	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
273	#107	—	79	2	no	—
274	C₄⋊C₈	D₃₁₆	1	1	yes	characteristic
275	#103	—	158	2	no	—
276	#102	—	158	2	no	—
277	#102	—	158	2	no	—
278	C₂²⋊C₈	D₃₁₆	1	1	yes	characteristic
279	C₂²⋊C₈	D₃₁₆	1	1	yes	characteristic
280	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
281	C₂⁴	—	316	2	no	—
282	#41	—	316	4	no	—
283	#41	—	632	2	no	—
284	C₂×Q₈	—	158	2	no	—
285	C₂×D₄	—	316	4	no	—
286	C₂×D₄	—	316	2	no	—
287	C₂×D₄	—	316	2	no	—
288	C₂×D₄	—	316	2	no	—
289	C₂×D₄	—	632	2	no	—
290	C₂×D₄	—	158	2	no	—
291	C₂×D₄	—	158	2	no	—
292	C₂×D₄	D₆₃₂	1	1	yes	characteristic
293	C₂²×C₄	—	316	2	no	—
294	C₂²×C₄	—	316	2	no	—
295	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
297	Q₁₆	—	158	2	no	—
298	Q₁₆	—	158	2	no	—
299	SD₁₆	—	316	4	no	—
300	SD₁₆	—	632	2	no	—
301	D₈	—	316	4	no	—
302	D₈	—	79	4	no	—
303	D₈	—	158	2	no	—
304	D₈	—	158	2	no	—
305	D₈	—	158	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
311	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
312	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
313	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
314	C₄⋊C₄	—	316	2	no	—
315	C₄⋊C₄	—	158	2	no	—
316	C₄⋊C₄	D₆₃₂	1	1	yes	characteristic
317	C₂²⋊C₄	—	316	2	no	—
318	C₂²⋊C₄	—	316	2	no	—
319	C₂²⋊C₄	—	316	2	no	—
320	C₂²⋊C₄	—	316	2	no	—
321	C₂²⋊C₄	—	316	2	no	—
322	C₂²⋊C₄	D₆₃₂	1	1	yes	characteristic
323	C₂²⋊C₄	D₆₃₂	1	1	yes	characteristic
324	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
325	C₁₆	—	2	1	no	—
326	C₁₆	—	2	1	no	—
327	C₁₆	—	2	1	no	—
328	C₁₆	D₄×D₇₉	1	2	yes	—
329	C₂³	—	316	2	no	—
330	C₂³	—	316	2	no	—
331	C₂³	—	632	4	no	—
332	C₂³	—	632	4	no	—
333	C₂³	—	1264	2	no	—
334	C₂³	C₂×D₆₃₂	1	1	yes	characteristic
335	C₂³	C₂×D₆₃₂	1	1	yes	characteristic
336	Q₈	—	316	2	no	—
337	Q₈	—	316	2	no	—
338	D₄	—	2	2	no	—
339	D₄	—	316	2	no	—
340	D₄	—	316	2	no	—
341	D₄	—	316	2	no	—
342	D₄	—	632	4	no	—
343	D₄	—	632	4	no	—
344	D₄	—	158	4	no	—
345	D₄	—	1264	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	316	2	no	—
351	C₂×C₄	—	316	2	no	—
352	C₂×C₄	—	632	4	no	—
353	C₂×C₄	—	1264	2	no	—
354	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
355	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
356	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
357	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	C₂×D₄×D₇₉	1	1	yes	characteristic
363	C₈	#14579207	1	1	yes	characteristic
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	316	4	no	—
370	C₂²	—	632	2	no	—
371	C₂²	—	632	2	no	—
372	C₂²	—	632	2	no	—
373	C₂²	—	632	2	no	—
374	C₂²	—	632	2	no	—
375	C₂²	—	1264	8	no	—
376	C₂²	#19098995	1	2	yes	complemented
377	C₂²	C₂²×D₆₃₂	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	632	2	no	—
383	C₄	—	632	2	no	—
384	C₄	D₄×D₃₁₆	1	1	yes	characteristic
385	C₄	#19099368	1	1	yes	characteristic
386	C₂	—	2	2	no	—
387	C₂	—	4	1	no	—
388	C₂	—	632	4	no	—
389	C₂	—	1264	2	no	—
390	C₂	D₄×D₆₃₂	1	1	yes	characteristic
391	C₂	C₂×#19098995	1	1	yes	characteristic
392	C₂	#23776541	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₆₃₂
commutator, cosocle	C₂×C₈×C₇₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	D₄×C₁₆×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₈
hypercenter	D₄×C₁₆	D₇₉
hypocenter	C₇₉	#33846
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄ ◁ D₄×C₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#19098995	C₂	semidirect
2. C₂²×D₁₂₆₄	C₂	semidirect
3. #23775087	C₂	semidirect
4. #23765661	C₂	semidirect
5. #23765491	C₂	semidirect
6. #23765486	C₂	semidirect
7. #23765456	C₂	semidirect
8. #23765331	C₂	semidirect
9. #23765325	C₂	semidirect
10. C₄×D₁₂₆₄	C₂	semidirect
11. D₄×C₁₆×C₇₉	C₂	semidirect
12. C₂×#14579183	C₂²	semidirect
16. C₂×Dic₆₃₂	C₂²	semidirect
17. C₂×#14579106	C₂²	semidirect
18. C₂×#14579106	C₂²	semidirect
23. #19098947	C₂²	semidirect
25. #19098799	C₂²	semidirect
29. C₄×D₆₃₂	C₂²	semidirect
30. #19098389	C₂²	semidirect
31. #19098368	C₂²	semidirect
32. #19098365	C₂²	semidirect
33. #19098365	C₂²	semidirect
35. C₂²×C₁₆×C₇₉	C₂²	semidirect
37. C₄⋊C₁₆×C₇₉	C₂²	semidirect
39. C₂²⋊C₁₆×C₇₉	C₂²	semidirect
40. C₄×C₁₆×C₇₉	C₂²	semidirect
66. D₁₂₆₄	D₄	semidirect
172. C₂²×C₇₉	#508	semidirect
207. D₄×C₁₆	D₇₉	semidirect
208. C₇₉	#33846	semidirect
221. C₂²×C₁₆	C₂×D₇₉	semidirect
231. C₄⋊C₁₆	C₂×D₇₉	semidirect
236. C₂²⋊C₁₆	C₂×D₇₉	semidirect
237. C₄×C₁₆	C₂×D₇₉	semidirect
376. C₂²	#19098995	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#19098995	2
C₂²×D₁₂₆₄	2
#23775087	2
#23765661	2
#23765491	2
#23765486	2
#23765456	2
#23765331	2
#23765325	2
C₄×D₁₂₆₄	2
D₄×C₁₆×C₇₉	2
#33846	79